A graph neural network and multi-task learning-based decoding algorithm for enhancing XZZX code stability in biased noise
Bo Xiao(肖博)1, Zai-Xu Fan(范在旭)1, Hui-Qian Sun(孙汇倩)1, Hong-Yang Ma(马鸿洋)2, and Xing-Kui Fan(范兴奎)2,†
1 School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266033, China; 2 School of Sciences, Qingdao University of Technology, Qingdao 266033, China
Abstract Quantum error correction is a technique that enhances a system's ability to combat noise by encoding logical information into additional quantum bits, which plays a key role in building practical quantum computers. The surface code, with only one stabilizer generator on each face, demonstrates significant application potential under biased noise. However, the existing minimum weight perfect matching (MWPM) algorithm has high computational complexity and lacks flexibility in large-scale systems. Therefore, this paper proposes a decoding method that combines graph neural networks (GNN) with multi-classifiers, the syndrome is transformed into an undirected graph, and the features are aggregated by convolutional layers, providing a more efficient and accurate decoding strategy. In the experiments, we evaluated the performance of the code under different biased noise conditions (, 20, 200) and different code distances (, 5, 7, 9, 11). The experimental results show that under low bias noise (), the GNN decoder achieves a threshold of 0.18386, an improvement of approximately 19.12% compared to the MWPM decoder. Under high bias noise (), the GNN decoder reaches a threshold of 0.40542, improving by approximately 20.76%, overcoming the limitations of the conventional decoder. They demonstrate that the GNN decoding method exhibits superior performance and has broad application potential in the error correction of code.
Fund: Project supported by the Natural Science Foundation of Shandong Province, China (Grant No. ZR2021MF049), the Joint Fund of Natural Science Foundation of Shandong Province, China (Grant Nos. ZR2022LL.Z012 and ZR2021LLZ001), and the Key Research and Development Program of Shandong Province, China (Grant No. 2023CXGC010901).
Corresponding Authors:
Xing-Kui Fan
E-mail: fanxingkui@126.com
Cite this article:
Bo Xiao(肖博), Zai-Xu Fan(范在旭), Hui-Qian Sun(孙汇倩), Hong-Yang Ma(马鸿洋), and Xing-Kui Fan(范兴奎) A graph neural network and multi-task learning-based decoding algorithm for enhancing XZZX code stability in biased noise 2025 Chin. Phys. B 34 050306
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